Nonequilbrium work by charge control in a Josephson junction

TL;DR

This paper investigates the nonequilibrium work in a Josephson junction under time-varying charge control, analyzing fluctuation theorems and the reliability of free energy estimations in different protocols.

Contribution

It provides a detailed analysis of fluctuation theorems in Josephson junctions with charge control, highlighting protocol-dependent reliability of free energy estimates.

Findings

The free energy change b4F is estimated as zero using Crooks and Bennett methods.

Jarzynski estimator error depends on protocol rapidity and duration.

Work and its average show saturation behaviors influenced by oscillatory phase dynamics.

Abstract

We consider a single Josephson junction in the presence of time varying gate charge, and examine the nonequilibrium work done by the charge control in the framework of fluctuation theorems. We obtain the probability distribution functions of the works performed by forward protocol and by its time reversed protocol, which from the Crooks relation gives the estimation of the free energy changes \Delta F =0. The reliability of \Delta F estimated from the Jarzynksi equality is crucially dependent on protocol parameters, while Bennett's acceptance ratio method confirms consistently \Delta F=0. The error of the Jarzynski estimator either grows or becomes saturated as the duration of the work protocol increases, which depends on the protocol rapidity determining the existence of the oscillatory motion of the phase difference across the junction. The average of the work also shows similar behaviors and its saturation value is given by the relative weight of the oscillatory trajectory with respect to running trajectories with constant acceleration. We discuss non-negativity of the work average and its relation to heat and entropy production associated with the circuit control.